Inference on the variance and smoothing of the paths of diffusions
Gonzalo Perera, Mario Wschebor (2002)
Annales de l'I.H.P. Probabilités et statistiques
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Gonzalo Perera, Mario Wschebor (2002)
Annales de l'I.H.P. Probabilités et statistiques
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Bogdan Iftimie, Étienne Pardoux, Andrey Piatnitski (2008)
Annales de l'I.H.P. Probabilités et statistiques
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This paper deals with the homogenization problem for a one-dimensional parabolic PDE with random stationary mixing coefficients in the presence of a large zero order term. We show that under a proper choice of the scaling factor for the said zero order terms, the family of solutions of the studied problem converges in law, and describe the limit process. It should be noted that the limit dynamics remain random.
D. Loukianova, O. Loukianov (2008)
Annales de l'I.H.P. Probabilités et statistiques
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Usually the problem of drift estimation for a diffusion process is considered under the hypothesis of ergodicity. It is less often considered under the hypothesis of null-recurrence, simply because there are fewer limit theorems and existing ones do not apply to the whole null-recurrent class. The aim of this paper is to provide some limit theorems for additive functionals and martingales of a general (ergodic or null) recurrent diffusion which would allow us to have a somewhat unified...
Jun Masamune, Toshihiro Uemura (2011)
Annales de l'I.H.P. Probabilités et statistiques
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Motivated by the recent development in the theory of jump processes, we investigate its conservation property. We will show that a jump process is conservative under certain conditions for the volume-growth of the underlying space and the jump rate of the process. We will also present examples of jump processes which satisfy these conditions.
David Pollard (2002)
Annales de l'I.H.P. Probabilités et statistiques
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